Sigma-delta analog-to-digital modulators, which can be used in a sigma-delta analog-to-digital converter (ADC) or a sigma-delta digital-to-analog converter (DAC), can provide a degree of shaping (filtering) of quantization noise that can be present. The higher the order of the sigma-delta modulator, the further the quantization noise is pushed into the frequency band, away from the signal being converted and the quantization noise. As such, sigma-delta ADCs and DACs (and their attendant modulators) have become popular in high frequency and high precision applications.
However, sigma-delta modulators do not offer noise shaping for noise that is due to a mismatch between the unity elements used in a DAC (referred to as a feedback DAC) that is a part of a feedback loop in the sigma-delta modulator and a quantizer. The mismatch can therefore be a problem in the sigma-delta modulator if it is of significant magnitude. The mismatch can result in an overall reduction in the signal-to-noise ratio (SNR) of the sigma-delta modulator.
One solution that can be used to reduce the mismatch that is present in the feedback DAC is to use a feedback DAC with high linearity. Ideally, the feedback DAC should have a linearity corresponding to the final resolution of the quantizer. A useful technique used to improve the DAC linearity is commonly referred to as dynamic element matching (DEM). Its use can reduce the mismatch in the sigma-delta modulator.
One disadvantage of the prior art is that if the feedback DAC has high resolution, then it can potentially be difficult to achieve an effective DEM. A high resolution feedback DAC may require a large number of elements, and too many elements to average can lead to tones in the signal band for signals with low input levels.
A second disadvantage of the prior art is that even if the mismatch can be transformed into noise, it can remain unshaped and become a component in the signal band, thus having an impact on the SNR of the sigma-delta modulator.